with \(e_k=\chi _k(t)-\widehat{\chi }(t)\)  where
\(\widehat{\chi }(t)=\frac{1}{N}\sum _k \chi _k(t)\)  denotes the empirical mean and \(\left(\chi _k(t)\right)_{k\in [1,N]}\)  is an ensemble of \(N\)  forecasts [1]}. This time, the numerical complexity scales with the number of ensemble members \(N\)  and the size of the problem \(n\) : the numerical cost of an ensemble of forecast is the cost of \(N\)  integrations of the model Eq. (REF ).
